Subgroups — C₁₁×D₁₀₈₅ #37558824

Order 23870.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₁×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₂₁₇	—	5	1	no	maximal, Hall
3	C₁₁×D₁₅₅	—	7	1	no	maximal, Hall
4	C₇×C₁₁×C₃₁	D₅	1	1	yes	characteristic, complemented, Hall
5	D₁₀₈₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₁₁×C₃₁	D₇	1	1	yes	characteristic, complemented, Hall
7	C₅×C₇×C₃₁	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
8	C₁₁×D₃₅	—	31	1	no	maximal, Hall
9	C₁₁×D₃₁	—	35	1	no	Hall
10	D₂₁₇	—	5	1	no	Hall
11	C₅×C₇×C₁₁	D₃₁	1	1	yes	characteristic, complemented, Hall
12	C₁₁×C₃₁	D₃₅	1	1	yes	characteristic, complemented, Hall
13	D₁₅₅	—	7	1	no	Hall
14	C₇×C₃₁	D₅×C₁₁	1	1	yes	characteristic, complemented, Hall
15	C₅×C₃₁	C₁₁×D₇	1	1	yes	characteristic, complemented, Hall
16	C₁₁×D₇	—	155	1	no	Hall
17	D₅×C₁₁	—	217	1	no	Hall
18	C₇×C₁₁	D₁₅₅	1	1	yes	characteristic, complemented, Hall
19	D₃₅	—	31	1	no	Hall
20	D₃₁	—	35	1	no	Hall
21	C₅×C₁₁	D₂₁₇	1	1	yes	characteristic, complemented, Hall
22	C₅×C₇	C₁₁×D₃₁	1	1	yes	characteristic, complemented, Hall
23	C₃₁	C₁₁×D₃₅	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₁₁	—	1085	1	no	Hall
25	D₇	—	155	1	no	Hall
26	C₁₁	D₁₀₈₅	1	1	yes	characteristic, direct product factor, Sylow
27	D₅	—	217	1	no	Hall
28	C₇	C₁₁×D₁₅₅	1	1	yes	characteristic, complemented, Sylow
29	C₅	C₁₁×D₂₁₇	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	1085	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁	D₁₀₈₅
commutator, cosocle, hypocenter	C₅×C₇×C₃₁	C₂×C₁₁
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₁×C₃₁	C₂
LCS	G ▷ C₅×C₇×C₃₁
UCS	C₁ ◁ C₁₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅×C₇×C₁₁×C₃₁	C₂	semidirect
4. C₇×C₁₁×C₃₁	D₅	semidirect
5. D₁₀₈₅	C₁₁	direct (N × H)
6. C₅×C₁₁×C₃₁	D₇	semidirect
7. C₅×C₇×C₃₁	C₂×C₁₁	semidirect
11. C₅×C₇×C₁₁	D₃₁	semidirect
12. C₁₁×C₃₁	D₃₅	semidirect
14. C₇×C₃₁	D₅×C₁₁	semidirect
15. C₅×C₃₁	C₁₁×D₇	semidirect
18. C₇×C₁₁	D₁₅₅	semidirect
21. C₅×C₁₁	D₂₁₇	semidirect
22. C₅×C₇	C₁₁×D₃₁	semidirect
23. C₃₁	C₁₁×D₃₅	semidirect
26. C₁₁	D₁₀₈₅	direct (N × H)
28. C₇	C₁₁×D₁₅₅	semidirect
29. C₅	C₁₁×D₂₁₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×C₇×C₁₁×C₃₁	2
C₁₁×D₂₁₇	5
C₁₁×D₁₅₅	7
D₁₀₈₅	11
C₁₁×D₃₅	31

Subgroups — C11×D1085 #37558824

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×D₁₀₈₅ #37558824